Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496412 | Journal of Number Theory | 2005 | 22 Pages |
Abstract
Let E be an elliptic curve defined over Q and PâE(Q) a rational point of infinite order. Suppose that E has complex multiplication by an order in the imaginary quadratic field k. Denote by ME,P the set of rational primes â such that â splits in k, E has good reduction at â, and P is a primitive point modulo â. Under the generalized Riemann hypothesis, we can determine the positivity of the density of the set ME,P explicitly.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yen-Mei J. Chen, Jing Yu,